The global positioning system (GPS) is a satellite-based navigation and time transfer system developed by the U.S. Department of Defense. It serves marine, airborne and terrestrial users.
The system includes GPS satellites that each transmit L1 and L2 GPS signals. The L1 and L2 GPS signals comprise modulated carrier signals at the GPS L1 and L2 frequencies (1,575 and 1,227 MHz) which are each modulated by a coarse-acquisition pseudo-random (C/A) code, an encrypted precision pseudo-random (P) code, and navigation data. The navigation data includes the transmitting GPS satellite's orbit location and clock offset from GPS time.
Since the P code is encrypted, it is unavailable to most users. However, a user can determine the pseudo-range to each GPS satellite in view based on the time of arrival of the C/A code contained by the GPS signals transmitted by the GPS satellite. The user can compute a position fix based on the determined pseudo-ranges to the GPS satellites in its view and the locations and clock offsets for these GPS satellites contained in the navigation data of the GPS signals they transmit.
However, the U.S. Department of Defense engages in selective availability and deliberately misrepresents the true location and clock offsets of the GPS satellites in the navigation data of the GPS signals they transmit. Moreover, the ionosphere and the troposphere delay the arrival of these GPS signals at the user's location. Thus, these factors affect the accuracy and integrity of GPS for the user.
In order to improve the accuracy and integrity of GPS, GPS may be augmented by a network of ground-based reference stations. The reference stations monitor the health of the GPS signals transmitted by the GPS satellites in their view and generate corrections to these signals which are then transmitted to the user. The user can accurately determine his position based on the GPS signals he receives from the GPS satellites and the corrections to these signals he receives from the reference stations. This form of GPS is known as differential GPS (DGPS).
A number of systems and methods have been developed for wide area DGPS (WDGPS). However, all of them suffer from various problems which render them undesirable.
One of these approaches is called position domain WDGPS and combines the information from multiple wide area reference stations (WRSs) in the position domain. Such an approach is described in "Multi-Site Real-Time DGPS System Using Staffix Link: Operational Results", by D. Lapucha and M. Huff, Proceedings of the Fifth International Technical Meeting of the Satellite Division of the Institute of Navigation, Albuquerque, September 1992.
In this approach, each WRS acts as a local area DGPS (LDGPS) reference station. Based on its known fixed position, it computes for each GPS satellite in view a corresponding pseudo-range correction to the GPS satellite. Each WRS then transmits a stream of LDGPS pseudo-range corrections to the user. The user computes pseudo-ranges to the GPS satellites in his view based on the GPS signals received from these GPS satellites. The user then applies the pseudo-range corrections to the computed pseudo-ranges. If there are M WRSs, the user computes M position fixes and the corresponding covariance matrices. The user then uses the covariance matrices to form a single weighted position fix.
However, this approach does not involve the estimation of any of the underlying states of the GPS satellites, namely GPS satellite ephemeris and clock errors. Nor does it involve the estimation of the clock differences between the different reference stations. These type of errors behave quite differently and could be mitigated if they were separated. Since this approach allows these errors to be combined, it unfortunately does not allow a-priori information about each of the underlying states to be introduced into the estimation process. As a result, the accuracy of each computed pseudo-range correction decreases rapidly with age and user to reference station separation.
Additionally, this approach requires M independent data streams to be sent to the user if there are M different reference stations. Thus, it requires a rather large data bandwidth to implement.
Another approach is called measurement domain WDGPS and combines the pseudo-range measurements from multiple WRSs. Such a system is described in "The FAA's WIBANDGPS Testbed and Recent Test Results", by M. Lage and B. Elrod, Proceedings of the Sixth International Technical Meeting of the Satellite Division of the Institute of Navigation, Salt Lake City, 1993, and in "GPS Wide Area Augmentation System (WAAS) Testbed Results--Phase ID Testbed Results", by F. Haas, M. Lage, and S. Kalinowski, Proceedings of the Annual Meeting of the Institute of Navigation, Colorado Springs, June 1994.
In this approach, each WRS computes a pseudo-range correction to each GPS satellite in view. These pseudo-range corrections are sent to a wide area master station (WMS) rather than the user. The WMS uses well known common view time transfer techniques to estimate the clock differences between the WRSs. The estimated clock differences are then removed from the pseudo-range corrections. As a result, these synchronized pseudo-range corrections are all referenced to a common master clock. The WMS then averages for each GPS satellite the synchronized pseudo-range corrections for the GPS satellite. These averaged pseudo-range corrections are then transmitted to the user and used by the user in the same way as described earlier for the position domain WDGPS approach.
The measurement domain WDGPS approach requires less data bandwidth than the position domain WDGPS approach since a single averaged data stream for each GPS satellite is sent to the user rather than M different data streams. However, in this approach as well, the pseudo-range corrections degrade rapidly with age and user to reference station separation since the underlying states of the GPS satellites are not estimated and therefore the user cannot leverage the known behavior of the underlying states to make accurate position fixes. This frailty is especially pronounced if the ephemeris errors associated with one or more of the GPS satellites is large or the ionosphere is introducing errors which vary spatially.
Still another approach is called state space WDGPS which uses the information from multiple WRSs to estimate the underlying states of the GPS satellites, the underlying state of the ionosphere, and the underlying clock differences between the WRSs. Such a system is described in "Algorithms and Implementation of Wide Area Differential GPS", by C. Kee and B. Parkinson, Proceedings of the Fifth International Technical Meeting of the Satellite Division of the Institute of Navigation, Albuquerque, September 1992, and also in "Wide Area Differential GPS (WADGPS)", by C. Kee, Stanford University, Ph.D Dissertation, December 1993.
In this approach as well, each WRS computes a pseudo-range residual (i.e., correction) for each GPS satellite in view. The computed pseudo-range residuals are sent to a WMS which uses one large estimator to simultaneously compute the clock differences between the WRSs and the ephemeris and clock corrections for the ephemeris and clock errors of each GPS satellite in view of the network.
The estimator in this approach must solve a system of equations which contains 4K+(M-1) unknowns and MK knowns, where K is the number of satellites in view and M is the number of reference stations. This stems from the fact that each satellite has 3 unknown components of ephemeris error and 1 unknown clock error. In addition, there are M-1 unknown offsets between the clocks of the WRSs clocks. At the same time, the system of equations contains MK knowns corresponding to the K pseudo-range residuals computed by each of the M WRSs.
When 4K+(M-1)&gt;MK, the system is under determined and the WMS must use a minimum norm solution. When 4K+(M-1)=MK, then the system is exactly specified and can be readily inverted. When 4K+(M-1)&lt;MK, then the system is over specified and the pseudo-inverse yields an estimate with minimum mean square error.
Unlike the previously discussed approaches, the state space WDGPS approach separates the underlying states of the system, and as such, it enables the use of a-priori models and side information for these states. However, its complexity impedes the straight forward integration of such models.
Moreover, it requires a greater data bandwidth than is necessary. This occurs, because the WRS network can be rather sparse and, as such, the system of equations used by the WMS is frequently under determined. Specifically, rising GPS satellites that have just appeared over the horizon are of great concern to WDGPS users because they can greatly improve the geometry and accuracy of the position fix. However, the system is always under determined in the case of a rising GPS satellite. Even though the minimum norm solution described above yields an accurate correction for a newly rising GPS satellite, the quickly varying components of the GPS satellite clock correction splatter into the GPS satellite ephemeris correction. Consequently, the ephemeris correction must be sent as frequently as the clock correction, thereby increasing the required data bandwidth.
A similar approach is described in U.S. Pat. No. 5,323,322 issued on Jun. 21, 1994 to Mueller, et. al. In this approach, ephemeris and clock corrections for a particular GPS satellite can be provided to a user only if the GPS satellite is observed by five or more WRSs. However, as indicated earlier, rising GPS satellites are very important to users since they provide added leverage for computing accurate position fixes. Thus, this approach is not capable of providing a user with ephemeris and clock corrections for newly rising GPS satellites.